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In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…

We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of…

We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…

We indicate a new approach to the optimization of the clamped plates with holes. It is based on the use of Hamiltonian systems and the penalization of the performance index. The alternative technique employing the penalization of the state…

We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…

In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The method is based on a Bernardi--Raugel-like $\boldsymbol{H}(\mathrm{div})$-conforming method proposed first for the Stokes flows in [Li…

We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…

One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. Recently, a new class of methods, named Hamiltonian Boundary…

We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…

We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…

We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…

Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…

Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness…

We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an…

We consider an overdetermined problem for Laplace equation on a disk with partial boundary data where additional pointwise data inside the disk have to be taken into account. After reformulation, this ill-posed problem reduces to a bounded…

This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…

We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…